Obfuscation of Abstract Data-Types - Rowan

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CHAPTER 2. OBFUSCATIONS FOR INTERMEDIATE LANGUAGE 27 gcd(int a, int b) { int i; int j; i = a; j = b; if (i * i > 0) {goto IL001a;} else {goto IL0016;} IL000c: if (i < j) {j -= i; continue;} IL0016: i -= j; IL001a: if (i == j) {return i;} else {goto IL000c;} } Figure 2.3: Output from Salamander However in IL, we are allowed to use branches to jump into loops (while loops do not, of course, occur in IL — they are achieved by using conditional branches). So, if we insert this kind of jump in IL, we will have a control flow graph which is irreducible and a naive decompiler could produce incorrect C# code. A smarter decompiler could change the while into an if statement that uses goto jumps. As we do not actually want this jump to happen, we use an opaque predicate that is always false. Let us look at the GCD example in Section 2.1.1 again. Suppose that we want to insert the jump: if ((x ∗ x) < 0) goto L; before the while loop where L is a statement in the loop. So, we need to put instructions in the IL file to create this: IL0100: ldloc.0 IL0101: ldloc.0 IL0102: mul IL0103: ldc.i4.0 IL0104: blt.s IL0010 The place that we jump to in the IL needs to be chosen carefully — a suitable place in the GCD example would be between the instructions IL0003 and IL0004. We must (obviously) ensure that it does actually jump to a place inside the while loop. Also, we must ensure that we do not interfere with the depth of the stack (so that we can still verify the program). Figure 2.3 shows the result of decompiling the resulting executable using the Salamander decompiler [45]. We can see that the while statement has been removed and in its place is a more complicated arrangement of ifs and gotos. This obfuscation as it stands is not very resilient. It is obvious that the conditional x ∗ x < 0 can never be true and so the jump into the loop never happens. 2.3 Transformation Toolkit In the last section we saw writing obfuscations for IL involved finding appropriate instructions and replacing all occurrences of these instructions by a set of
CHAPTER 2. OBFUSCATIONS FOR INTERMEDIATE LANGUAGE 28 new instructions. This replacement is an example of a rewrite rule [32]: L ⇒ R if c which says that if the condition c is true then we replace each occurrence of L with R. This form of rewrite rule can be automated and we summarise the transformation toolkit described in [22] to demonstrate one way of specifying obfuscations for IL. This toolkit consists of three main components: • A representation of IL, called EIL, which makes specifying transformations easier. • A new specification language, called Path Logic Programming, which allows us to specify program transformations on the control flow graph. • A strategy language with which we can control how the transformations are applied. We briefly describe these components (more details can be found in [22]) before specifying some of the generalised obfuscations given in Section 1.3. 2.3.1 Path Logic Programming Path Logic Programming (PLP) is a new language developed for the specification of program transformations. PLP extends Prolog [51] with new primitives to help express the side conditions of transformations. The Prolog program will be interpreted relative to the flow graph of the object program that is being transformed. One new primitive is all Q (N ,M) which is true if N and M are nodes in the flow graph, and all paths from N to M are of the form specified by the pattern Q. Furthermore, there should be at least one path that satisfies the pattern Q. This is to stop a situation where we do not have a path between N and M and so the predicate all Q (N ,M) will be vacuously true. Similarly, the predicate exists Q (N ,M) is true if there exists a path from N to M which satisfies the pattern Q. As an example of all, consider: all ( { }∗; { ′ set(X,A), local(X)}; { not ( ′ def (X)) }∗; { ′ use(X)} ) (entry,N) This definition says that all paths from the program entry to node N should satisfy a particular pattern. A path is a sequence of edges in the flow graph. The pattern for a path is a regular expression and in the above example the regular expression consists of four components:
Page 1 and 2: Obfuscation of Abstract Data-Types
Page 3 and 4: Contents I The Current View of Obfu
Page 5 and 6: 5.4.3 Third Definition . . . . . .
Page 7 and 8: List of Figures 1 An example of obf
Page 9 and 10: 8 public class c { d t1 = new d();
Page 11 and 12: 10 • Obfuscations can be proved c
Page 13 and 14: Chapter 1 Obfuscation Scully: “No
Page 15 and 16: CHAPTER 1. OBFUSCATION 14 These thr
Page 17 and 18: CHAPTER 1. OBFUSCATION 16 by changi
Page 19 and 20: CHAPTER 1. OBFUSCATION 18 We could
Page 21 and 22: CHAPTER 1. OBFUSCATION 20 B 1 [0] =
Page 23 and 24: Chapter 2 Obfuscations for Intermed
Page 25 and 26: CHAPTER 2. OBFUSCATIONS FOR INTERME
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Chapter 5 Sets and the Splitting Bu
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CHAPTER 5. SETS AND THE SPLITTING 9
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CHAPTER 6. THE MATRIX OBFUSCATED 10
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Chapter 8 Conclusions and Further W
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CHAPTER 8. CONCLUSIONS AND FURTHER
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CHAPTER 8. CONCLUSIONS AND FURTHER
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BIBLIOGRAPHY 140 [13] Thomas H. Cor
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BIBLIOGRAPHY 142 [43] Simon Peyton
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Appendix A List assertion We want t
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APPENDIX A. LIST ASSERTION 146 Case
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APPENDIX A. LIST ASSERTION 148 For
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APPENDIX A. LIST ASSERTION 150 Case
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APPENDIX A. LIST ASSERTION 152 1 +
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APPENDIX A. LIST ASSERTION 154 0 +
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APPENDIX A. LIST ASSERTION 156 The
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APPENDIX A. LIST ASSERTION 158 The
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APPENDIX B. SET OPERATIONS 160 Now
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APPENDIX B. SET OPERATIONS 162 Proo
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APPENDIX B. SET OPERATIONS 164 B.2
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Appendix C Matrices We prove the as
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APPENDIX C. MATRICES 168 Base Case
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APPENDIX D. PROVING A TREE ASSERTIO
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APPENDIX E. OBFUSCATION EXAMPLE 186
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